If they killed her when she was that young there would have been nothing stopping Rittenhouse from finding someone else. Plus Lucy’s mother would still have known about Jessica’s brother and brought him back anyway. Also there were benefits for Emma’s existence for the time team, Emma worked for mason industries and helped build the time machines and in the Ms Sherlock Holmes episode, she could have easily killed the time team but she didn’t due to her own reasons with her mother, obviously like I said before Rittenhouse could have gotten someone else to do those things, however the possibility that the replacement wouldn’t kill Rufus and Flynn in the Ms Sherlock Holmes episode is almost impossible due to the unlikeliness that they could have had the exact same motive. Basically what I’m trying to say is if you eliminate Emma from Timeless then the plot would be exactly the same or the Time team would lose.

Thanks!